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Search: id:A108291
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| A108291 |
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Triangle, read by rows, resulting from the matrix product of triangle A108267 with Pascal's triangle (A007318). |
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+0
3
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| 1, 2, 1, 9, 9, 1, 64, 96, 34, 1, 625, 1250, 750, 125, 1, 7776, 19440, 16470, 5265, 461, 1, 117649, 352947, 386561, 184877, 35329, 1715, 1, 2097152, 7340032, 9863168, 6307840, 1913408, 232288, 6434, 1, 43046721, 172186884, 274223556, 220016574
(list; table; graph; listen)
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OFFSET
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0,2
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COMMENT
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Row sums form A108292. Column 0 is A000169(n) = (n+1)^n. Triangle with rows reversed is A108290.
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EXAMPLE
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Triangle begins:
1;
2,1;
9,9,1;
64,96,34,1;
625,1250,750,125,1;
7776,19440,16470,5265,461,1;
117649,352947,386561,184877,35329,1715,1;
2097152,7340032,9863168,6307840,1913408,232288,6434,1; ...
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PROGRAM
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(PARI) {T(n, k)=local(X=x+x*O(x^(n-k))); polcoeff(sum(j=0, n, binomial(n+n*j+j, n*j+j)*(x/(1+X))^j)/(1+X), n-k)}
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CROSSREFS
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Cf. A108267, A060543, A108290, A000169.
Sequence in context: A133175 A042977 A108290 this_sequence A019615 A132744 A059604
Adjacent sequences: A108288 A108289 A108290 this_sequence A108292 A108293 A108294
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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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