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A082578 A binomial sum. 3
1, 7, 67, 767, 9587, 126011, 1711595, 23796515, 336666215, 4828084575, 69994481871, 1023793569567, 15086216016367, 223704570996367, 3335098322412367, 49954148031128767, 751296616443141667 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

LINKS

Vincenzo Librandi, Table of n, a(n) for n = 0..200

FORMULA

a(n) = sum(k=0..n, binomial(2*k, k) * binomial(2*k+1,k)).

Recurrence: (n+3)*(n+2)*a(n+2) - (17*n^2+69*n+66)*a(n+1) + (16*n^2+64*n+60)*a(n) = 0.

a(n) ~ 2^(4*n+5)/(15*Pi*n). - Vaclav Kotesovec, Oct 14 2012

MATHEMATICA

Table[Sum[Binomial[2k, k]*Binomial[2k+1, k], {k, 0, n}], {n, 0, 20}] (* Vaclav Kotesovec, Oct 14 2012 *)

PROG

(Maxima) makelist(sum(binomial(2*k, k)*binomial(2*k+1, k), k, 0, n), n, 0, 12);

CROSSREFS

Partial sums of A000894.

Sequence in context: A199756 A038386 A243675 * A291814 A253386 A082698

Adjacent sequences:  A082575 A082576 A082577 * A082579 A082580 A082581

KEYWORD

easy,nonn

AUTHOR

Emanuele Munarini, May 07 2003

STATUS

approved

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Last modified February 24 09:40 EST 2020. Contains 332209 sequences. (Running on oeis4.)