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Search: id:A108290
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| A108290 |
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Triangle, read by rows, such that row n equals the inverse binomial transform of row n of table A060543, where A060543(n,k) = C(n+n*k+k, n*k+k). |
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4
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| 1, 1, 2, 1, 9, 9, 1, 34, 96, 64, 1, 125, 750, 1250, 625, 1, 461, 5265, 16470, 19440, 7776, 1, 1715, 35329, 184877, 386561, 352947, 117649, 1, 6434, 232288, 1913408, 6307840, 9863168, 7340032, 2097152, 1, 24309, 1513656, 18921924, 92365758, 220016574
(list; table; graph; listen)
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OFFSET
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0,3
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COMMENT
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Row sums form A108292. Main diagonal is A000169(n) = (n+1)^n. Triangle with rows reversed is A108291.
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EXAMPLE
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BINOMIAL[1,9,9] = {1,10,28,55,91,136,190,253,...}.
BINOMIAL[1,34,96,64] = {1,35,165,455,969,1771,2925,...}.
BINOMIAL[1,125,750,1250,625] = {1,126,1001,3876,10626,...}.
Triangle begins:
1;
1,2;
1,9,9;
1,34,96,64;
1,125,750,1250,625;
1,461,5265,16470,19440,7776;
1,1715,35329,184877,386561,352947,117649;
1,6434,232288,1913408,6307840,9863168,7340032,2097152; ...
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PROGRAM
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(PARI) {T(n, k)=local(X=x+x*O(x^k)); polcoeff(sum(j=0, n, binomial(n+n*j+j, n*j+j)*(x/(1+X))^j)/(1+X), k)}
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CROSSREFS
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Cf. A108267, A060543, A108290, A000169.
Sequence in context: A133169 A133175 A042977 this_sequence A108291 A019615 A132744
Adjacent sequences: A108287 A108288 A108289 this_sequence A108291 A108292 A108293
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KEYWORD
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nonn,tabl
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AUTHOR
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Paul D. Hanna (pauldhanna(AT)juno.com), May 31 2005
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