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Search: id:A125274
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| A125274 |
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Eigensequence of triangle A078812: a(n) = Sum_{k=0..n-1} A078812(n-1,k)*a(k) for n>0 with a(0)=1. |
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+0
2
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| 1, 1, 3, 10, 42, 210, 1199, 7670, 54224, 418744, 3499781, 31425207, 301324035, 3069644790, 33078375153, 375634524357, 4480492554993, 55971845014528, 730438139266281, 9935106417137098, 140553930403702487
(list; graph; listen)
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OFFSET
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0,3
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FORMULA
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a(n) = Sum_{k=0..n-1} C(n+k,n-k-1)*a(k) for n>0 with a(0)=1.
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EXAMPLE
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a(3) = 3*(1) + 4*(1) + 1*(3) = 10;
a(4) = 4*(1) + 10*(1) + 6*(3) + 1*(10) = 42;
a(5) = 5*(1) + 20*(1) + 21*(3) + 8*(10) + 1*(42) = 210.
Triangle A078812(n,k) = C(n+k+1,n-k) begins:
1;
2, 1;
3, 4, 1;
4, 10, 6, 1;
5, 20, 21, 8, 1;
6, 35, 56, 36, 10, 1; ...
where g.f. of column k = 1/(1-x)^(2*k+2).
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PROGRAM
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(PARI) a(n)=if(n==0, 1, sum(k=0, n-1, a(k)*binomial(n+k, n-k-1)))
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CROSSREFS
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Cf. A078812; A125273 (variant).
Sequence in context: A094195 A091843 A007552 this_sequence A030903 A030816 A030964
Adjacent sequences: A125271 A125272 A125273 this_sequence A125275 A125276 A125277
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KEYWORD
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nonn
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AUTHOR
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Paul D. Hanna (pauldhanna(AT)juno.com), Nov 26 2006
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