A086717 Convolution of primes with partition numbers.

2, 7, 17, 36, 69, 124, 209, 340, 532, 818, 1222, 1800, 2601, 3708, 5213, 7253, 9982, 13617, 18406, 24696, 32881, 43495, 57159, 74696, 97057, 125479, 161413, 206697, 263501, 334554, 423066, 533022, 669125, 837140, 1043880, 1297663, 1608234, 1987457, 2449246, 3010357

Offset

1,1

Links

Andrew Howroyd, Table of n, a(n) for n = 1..10000

Formula

a(n) = Sum_{k=1..n} A000041(k)*A000040(n+1-k). - Andrew Howroyd, Oct 29 2025

Prog

(PARI) seq(n)=Vec(sum(k=1, n, numbpart(k)*x^k, O(x*x^n))*sum(k=1, n, prime(k)*x^k)) \\ Andrew Howroyd, Oct 29 2025

Crossrefs

Cf. A000040, A000041.

Sequence in context: A318054 A033937 A116576 * A023657 A045380 A086321

Adjacent sequences: A086714 A086715 A086716 * A086718 A086719 A086720

Keyword

nonn

Author

Jon Perry, Jul 29 2003

Extensions

a(31) onward from Andrew Howroyd, Oct 29 2025

Status

approved